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ANALYTICAL MECHANICS
- 117.: Center of Mass of Filaments.  The transverse dimensions of a filament are supposed to be negligible; therefore " it can be treated as a geometrical curve.   Taking a piece of :; length ds as the element of mass and denoting the mass per "jLuait length by X we have
^:                                dm = X ds.
ILLUSTRATIVE EXAMPLE.
Find the center of mass of a semicircular filament.
(a) Taking x2, + y2 = a2 to be the equation of the circle we get
dm = X ds
-x\A+(!)'*
' Xa
dx
Va2-;
ds
FIG. 79.
(b) Referring the circle to polar coordinates we have r = a for its equation.   Therefore
dm = X ds
x\adB
T2
/